The absolute order of a permutation representation of a Coxeter group

2011/12/05 by Christos A. Athanasiadis, Athanasiadis, Christos A., Yuval Roichman +1
Mathematics · #05E15 #20F55 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:05E15 #msc:20F55

paper · pdf · doi:10.48550/arxiv.1112.0856

23 pages, 1 figure, revised version to be published in J. Algebraic Combinatorics

arxiv created 2013/03/07 · arxiv updated 2013/03/08

Abstract

A permutation representation of a Coxeter group W naturally defines an absolute order. This family of partial orders (which includes the absolute order on W) is introduced and studied in this paper. Conditions under which the associated rank generating polynomial divides the rank generating polynomial of the absolute order on W are investigated when W is finite. Several examples, including a symmetric group action on perfect matchings, are discussed. As an application, a well-behaved absolute order on the alternating subgroup of W is defined.

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